Question

in a regular polygon the ratio of the inner and outer angles in a vertex is 3:1,then

a) what is the sum of outer and inner angles at a vertex

b) find the measure of one outer angles

c) find the number of sides of the polygon​

Answer 1

Answer:

Since the given two angles are in the ratio 7:2 their actual values can be taken as 7x° and 2x°.

Since they form linear pair, 7x+2x = 180°=> 9x= 180° => x = 20°

Hence the interior angle = 7x° = 140° and the exterior angle is = 2x°= 40°.

Number of sides of the polygon = 360/each exterior angle = 360/40 = 9.